Question: Rewrite as a simplified fraction. ${3.6\overline{91} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3691.9191...\\ 10x &= 36.9191...\end{align*}}$ Subtracting the two equations, we have: ${990x = 3655}$ ${x = \dfrac{3655}{990}} $ ${x = \dfrac{731}{198}} \text{or} {3 \dfrac{137}{198}}$